A Torelli Theorem for log Calabi--Yau threefolds

TL;DR

This paper proves a Torelli theorem for a class of three-dimensional log Calabi--Yau pairs, establishing a link between their geometric structures and their Hodge-theoretic data.

Contribution

It introduces a Torelli theorem for log Calabi--Yau threefolds with maximal boundary, expanding understanding of their geometric and Hodge-theoretic properties.

Findings

Proves a generic Torelli theorem for certain log Calabi--Yau threefolds.

Establishes a correspondence between geometric structures and Hodge data.

Advances the classification of log Calabi--Yau pairs.

Abstract

We prove a generic Torelli theorem for a class of three-dimensional log Calabi--Yau pairs $(Y, D)$ with maximal boundary.